Question

1. use the net to find the surface area of the prism.

(options: 584 in², 40 in², 300 in², etc.)

Explanation:

Step1: Identify net shapes

The net has 2 rectangles (5×12, 8×13), 2 triangles, and 1 middle rectangle (12×8).

Step2: Calculate triangle area

Base=8in, height=12in. Area: $\frac{1}{2}×8×12=48$ in². Two triangles: $2×48=96$ in².

Step3: Calculate rectangle areas

5×12=60 in²; 8×13=104 in²; 12×8=96 in². Sum: $60+104+96=260$ in².

Step4: Total surface area

Add triangle and rectangle areas: $96+260=356$? Wait, correction: net has 2 triangles, 3 rectangles (5×12, 12×8, 8×13) and 2 more rectangles? No, correct net for triangular prism: 2 congruent triangles, 3 rectangles. Wait, original net: triangles (base8, height12), rectangles: 8×13, 12×13, 5×13? Wait, 13 is length. So triangle area: 2×(1/2×8×12)=96. Rectangles: 8×13 +12×13 +5×13=13×(8+12+5)=13×25=325. Total:96+325=421? No, image shows 5in,12in,13in,8in. Correct: triangles (8×12/2×2=96), rectangles: 5×13,12×13,8×13 →13×(5+12+8)=13×25=325. 96+325=421? No, option has 584. Wait, maybe 12×8×2 +5×12 +8×13 +12×13 +5×13? No, correct: surface area of triangular prism=2×triangle area + perimeter×length. Triangle area=48, perimeter=5+12+13=30, length=8. So 2×48 +30×8=96+240=336? No. Wait, image net: top rectangle 5×8, middle rectangle12×8, bottom rectangle13×8, two triangles 8×12/2. So total:5×8 +12×8 +13×8 +2×(8×12/2)=8×(5+12+13)+96=8×30+96=240+96=336? No. Wait option 584: 12×13×2 +8×13×2 +5×12×2? No. Wait maybe I misread: 5,12,13 are sides of triangle, length 8. So surface area=2×(1/2×5×12)+(5+12+13)×8=60 +30×8=60+240=300. Oh! 5×12/2×2=60, perimeter 30×8=240, total 300. Yes! 300 is option. So answer is 300 in².

Step1: Calculate triangle area

2×($\frac{1}{2}$×5×12)=60 in²

Step2: Calculate rectangle area

(5+12+13)×8=30×8=240 in²

Step3: Total surface area

60+240=300 in²

Answer:

584 in²